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This paper proposes a dual-supervised uncertainty inference (DS-UI) frameworkfor improving Bayesian estimation-based uncertainty inference (UI) in deepneural network (DNN)-based image recognition. In the DS-UI, we combine theclassifier of a DNN, i.e., the last fully-connected (FC) layer, with a mixtureof Gaussian mixture models (MoGMM) to obtain an MoGMM-FC layer. Unlike existingUI methods for DNNs, which only calculate the means or modes of the DNNoutputs' distributions, the proposed MoGMM-FC layer acts as a probabilisticinterpreter for the features that are inputs of the classifier to directlycalculate the probability density of them for the DS-UI. In addition, wepropose a dual-supervised stochastic gradient-based variational Bayes (DS-SGVB)algorithm for the MoGMM-FC layer optimization. Unlike conventional SGVB andoptimization algorithms in other UI methods, the DS-SGVB not only models thesamples in the specific class for each Gaussian mixture model (GMM) in theMoGMM, but also considers the negative samples from other classes for the GMMto reduce the intra-class distances and enlarge the inter-class marginssimultaneously for enhancing the learning ability of the MoGMM-FC layer in theDS-UI. Experimental results show the DS-UI outperforms the state-of-the-art UImethods in misclassification detection. We further evaluate the DS-UI inopen-set out-of-domain/-distribution detection and find statisticallysignificant improvements. Visualizations of the feature spaces demonstrate thesuperiority of the DS-UI.

DS-UI: Dual-Supervised Mixture of Gaussian Mixture Models for Uncertainty Inference in Image Recognition